Page 139 - Ganit Kaushal

Ex 10. The game of ‘Dahi-Vada’ is played with two different numbers. The players say ‘Dahi’ for multiples of
the smaller number, ‘Vada’ for multiples of the larger number and ‘Dahi-Vada’ for common multiples.
Players ended up saying just ‘Dahi’ or ‘Dahi-Vada’ and nobody said just ‘Vada’.

(a) What do you understand by that?
(b) If one of the numbers was 4, what should be the other number? (NCERT)
Sol. (a) The smaller number is a factor of the larger number.

(b) If one number is 4, the other should be 8 or 2. If 4 is smaller, then it’s 8; if 4 is larger, then it’s 2.
Ex 11. The “Dahi-Vada Game” is played up to 30. Multiples Multiples Multiples Multiples
The Fig. 1 is drawn related to the “Dahi-Vada of 3 of 5 of 3 of 5
Game” showing multiples of 3, multiples of 21 18 10 21 18 54 10
5 and common multiples of 3 and 5. Draw a 3 24 30 5 3 42 39 30 35 5
45
24
similar figure if the game is played till 60. 9 6 15 25 6 48 33 15 40 55
51
20
25
9
(NCERT) 12 20 12 36 60 50
27 27 57
Sol. If the game is played till 60, a similar Fig. 2 Common multiples of 3 and 5 Common multiples of 3 and 5
that we will get is given. Notice that common Fig. 1 Fig. 2
multiples of 3 and 5 are in the common region
of the two circles, multiples of 3 are on the left, and multiples of 5 are on the right.
Ex 12. In the Fig. 3, Guna has erased all the numbers Multiples Multiples Multiples Multiples
except the common multiples. Find out what those of ___ of ___ of 3 of 8
numbers could be and fill in the missing numbers 3 8
9
in the empty regions. (NCERT) 72 12 72 16
48
48
32
40
15
Sol. The Fig. 4 shows that the LCM of the numbers = 24 ___ 24 ___
24. \ The missing numbers are the two numbers
having their LCM = 24. So, there can be many Common multiples Common multiples
answers to this question. Fig. 3 Fig. 4
We know that LCM (3, 8) = 3 × 8 = 24.

\ Missing numbers are 3, 8 and one possible figure can be as given alongside. Readers are advised
to explore other cases. (Hint: LCM (6, 8) = 24; LCM (8, 12) = 24)
Ex 13. Find two numbers whose sum is 19 and whose product is 48.

Sol. The product of two numbers is 48. We have 48 = 1 × 48 = 2 × 24 = 3 × 16 = 4 × 12 = 6 × 8.
Out of them, only 16 and 3 have a sum = 19. \ The two numbers are 16, 3.

Exercise 5.1

1. Find the common factors of
(a) 35 and 50 (b) 56 and 120 (NCERT)
2. Find the common multiples of 4, 8, and 12 that lie between 50 and 100.

3. If the ‘Dahi-Vada’ game is played for the numbers from 1 to 105, find out:
(a) How many times would the children say ‘Dahi’, excluding the times they say ‘Dahi-Vada’?
(b) How many times would the children say ‘Vada’, excluding the times they say ‘Dahi-Vada’?
(c) How many times would the children say ‘Dahi-Vada’?

Prime Time 137